A dynamic risk assessment method for ship conflict based on imperfect information game theory

Ships are unlikely to share their navigation plans at sea, and officers on watch (OOWs) iteratively make decisions to avoid collisions based on limited information and predicted intention. Therefore, ship-ship collision avoidance can be considered a dynamic imperfect information game. Existing conflict risk assessment methods have focused on the uncertainty of ship motion and did not consider game behavior and the bounded rationality of OOWs. This paper proposes a novel dynamic risk assessment method based on the quantal response equilibrium, a modified game-theory model with imperfect information. Expected utility function is employed to quantify the behavior (yielding or not yielding) benefits, incorporating objective risk, energy loss and predicted intention. The OOWs' behavior probability is predicted by considering perception and intention uncertainties. We develop three stages to describe the OOWs' decisions in different risk zones from conflict formation to the end of collision avoidance. Dynamic conflict risk is estimated by calculating the joint probability that OOWs do not yield when encountering ships in the three stages based on the game theory. Simulations and a case study demonstrate that the method realistically reflects conflict risk and reveals ship characteristics influencing yielding. The results provide information for maritime traffic management and OOW training.